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Zorluk: ZorSeries Circuits

An aircraft avionics sensor circuit is powered by a 28 V28\text{ V} direct current (DC) power source connected in series with three resistors: R1=30 ΩR_1 = 30\ \Omega, R2=45 ΩR_2 = 45\ \Omega, and an unknown resistor R3R_3. A technician measures the voltage drop across R2R_2 and finds it to be 9 V9\text{ V}. Based on these circuit measurements, what are the total loop current and the resistance value of R3R_3?

Cevap:The total current flowing through the circuit is 【0.2】 A, and the resistance value of R3R_3 is 【65】 Ω\Omega.

Cevap

The circuit current is 0.2 A and the resistance of resistor R3 is 65 ohms.
Because the circuit components are connected in series, the current flowing through R2R_2 (I=9 V/45 Ω=0.2 AI = 9\text{ V} / 45\ \Omega = 0.2\text{ A}) is the exact same current passing through the entire loop. Applying Ohm's Law to the full circuit gives a total resistance of RT=28 V/0.2 A=140 ΩR_T = 28\text{ V} / 0.2\text{ A} = 140\ \Omega. Subtracting the known resistances (30 Ω+45 Ω=75 Ω30\ \Omega + 45\ \Omega = 75\ \Omega) leaves 65 Ω65\ \Omega for R3R_3.

Adım Adım Çözüm

1
Calculate the constant loop current using the known values for resistor R2R_2
I=V2R2=9 V45 Ω=0.2 AI = \frac{V_2}{R_2} = \frac{9\text{ V}}{45\ \Omega} = 0.2\text{ A}
In a series circuit, current is identical through every component.
2
Calculate the total equivalent resistance of the entire series circuit using Ohm's Law and the source voltage
RT=VsourceI=28 V0.2 A=140 ΩR_T = \frac{V_{\text{source}}}{I} = \frac{28\text{ V}}{0.2\text{ A}} = 140\ \Omega
Total circuit resistance equals the total applied voltage divided by the common series current.
3
Determine the resistance of R3R_3 by subtracting known series resistances from total resistance
R3=RT−(R1+R2)=140 Ω−(30 Ω+45 Ω)=140 Ω−75 Ω=65 ΩR_3 = R_T - (R_1 + R_2) = 140\ \Omega - (30\ \Omega + 45\ \Omega) = 140\ \Omega - 75\ \Omega = 65\ \Omega
Total series resistance is the direct algebraic sum of all individual resistances in the loop.

Anahtar Kavram

In a single-loop series circuit, current is constant at all points (IT=I1=I2=I3I_T = I_1 = I_2 = I_3), and total circuit resistance is the sum of all individual resistances (RT=R1+R2+R3R_T = R_1 + R_2 + R_3).
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